Question

Convert 3.3636 to a fraction. the .3636 is repeating

Answer 1

$x=3.363636...\qquad\text{multiply both sides by 100}\\\\100x=336.363636...\qquad\text{Make a difference}\\\\100x-x=336.363636...-3.363636...\\\\99x=333\qquad\text{divide both sides by 99}\\\\x=\dfrac{333:9}{99:9}\\\\\boxed{x=\dfrac{37}{11}}\\\\Answer:\ \boxed{3.\overline{36}=\dfrac{37}{11}=3\dfrac{4}{11}}$